Method for encrypting a calculation using a modular function
The invention concerns a method for encrypting, with a random quantity (r), a calculation using at least a modular operation ( 3 ), the method consisting in multiplying a first modulo (n) by said random quantity, in taking as modulo of the operation, the result (m) of said multiplication and in carrying out a modular reduction of the result of the operation, on the basis of the first modulo (n).
1. A method for scrambling, by means of a random value, a calculation involving a modular operation to be performed by an electronic circuit, the method comprising:
accepting as an input to the electronic circuit at least one input datum;
multiplying a first modulo by said random value to yield a product;
performing the modular operation to yield a first result, the modular operation using as operands the product of the multiplication and the at least one input datum;
performing a modular reduction, using the first modulo as an operand, of the first result of the modular operation, the modular reduction yielding a second result; and
outputting, from the electronic circuit, the second result of the modular reduction.
2. The method of claim 1 , wherein said modular operation involves the at least one input datum as well as at least one secret datum.
3. The method of claim 2 wherein said secret datum is contained in the electronic circuit implementing the method.
4. A circuit for scrambling a calculation performed by an integrated circuit, comprising:
an input terminal adapted to receive an input value;
a processing circuit adapted to perform processing steps on the value, the processing steps comprising
multiplying a first modulo by said random value to yield a product,
performing a modular operation to yield a first result using as operands the product of the multiplication and the value,
performing a modular reduction, using the first modulo as an operand, of the first result of the modular operation, the modular reduction yielding a second result, and
storing the second result as a result of the processing steps; and
an output terminal adapted to output the result of the processing steps.
5. The circuit of claim 4 , wherein the processing circuit is a microcontroller and the circuit further comprises at least one memory storing computer-executable instructions to be executed by the microcontroller.
6. The circuit of claim 4 , wherein the processing circuit is a hard-wired logic state machine.
7. The circuit of claim 4 , farther comprising at least one memory storing a secret datum.
8. A method of protecting a secret datum and an authentication calculation to be performed by an electronic circuit based at least in part on the secret datum, the method comprising:
accepting as input to the electronic circuit an input value;
determining a random value;
multiplying a first value by the random value to calculate a first operand;
performing the authentication calculation on the input value, the authentication calculation comprising a first modulo operation using the first operand as a divisor, the first modulo operation calculating a second operand;
determining a result by performing a second modulo operation using the second operand as a dividend and the first value as a divisor; and outputting, from the electronic circuit, the result.
9. The method of claim 8 , wherein the random value is determined by a pseudo-random process.
10. The method of claim 8 , wherein the random value is only used in the act of multiplying.
11. The method of claim 8 , further comprising clearing the random value from memory immediately following the act of multiplying.
12. The method of claim 8 , wherein the authentication calculation comprises at least one operation involving the input value and a secret datum.